David Cameron is on course for a possible general election win, according to a Guardian/ICM poll published today that shows support for the Conservatives climbing to a lead that could give them a narrow majority in the Commons, while Labour has plunged to a 19-year low.

The Tories have gained over the last month while support for Labour has fallen heavily in the wake of the recent alleged terror plot against airlines. An overwhelming majority of voters appear to pin part of the blame for the increased threat on Tony Blair's policy of intervention in Iraq and Afghanistan.

Ministers - including Mr Blair - have repeatedly denied that there is a connection. But 72%, including 65% of Labour voters, think government policy has made Britain more of a target for terrorists. Only 1% of voters believe the government's foreign policy has made Britain safer, a devastating finding given that action in Iraq and Afghanistan has been justified in part to defeat Islamist terrorism.

That may explain why Labour support has dropped four points in a month, to 31%, the lowest figure recorded by ICM for the Guardian since just before the 1987 election and the second lowest since the poll series began in 1984. The fall may be partly caused by Mr Blair's absence on holiday and public unhappiness at the announcement that John Prescott would stand in. The rating is worse than Labour achieved at the 1987 or 1992 elections and worse than almost every poll result under Neil Kinnock and John Smith's leadership.

Meanwhile the Conservatives have climbed one point to 40%, passing the confidence-boosting threshold for the first time in a Guardian/ICM poll since August 1992, in the wake of John Major's election victory.

The findings will shock many at Westminster who had expected Labour to gain ground following John Reid's high-profile handling of the alleged plot against transatlantic airlines. Carried out over the past weekend, following the series of terror arrests, the poll shows voters do not believe the government is giving an honest account of the threat facing Britain. Only 20% of all voters, and 26% of Labour voters, say they think the government is telling the truth about the threat, while 21% of voters think the government has actively exaggerated the danger.

A majority, 51%, say the government is not giving the full truth and may be telling less than it knows. That finding comes despite a newly introduced system of public information warnings that saw the home secretary downgrade the threat level from critical to severe.

Such distrust forms the background to a dramatic shift of support away from Labour. The poll shows former Labour voters switching to the Conservatives and Liberal Democrats in almost equal numbers, boosting Lib Dem support by five points to 22%.

The findings will help the party's leader, Sir Menzies Campbell, ahead of what is expected to be a testing party conference next month. The poll follows his questioning of the prime minister's close alliance with George Bush and could leave the Lib Dems as powerbrokers if the election produces a close result.

The poll also contains evidence of an underlying strengthening of support for the Tories. It is the second Guardian/ICM poll in a row suggesting they have finally shaken off the Black Wednesday factor which has dogged them for 14 years.

The voting figures, if repeated at a general election, would send Mr Cameron to Downing Street with a majority of around 10 - although that could climb if Liberal Democrat discontent with the government costs Labour tactical votes in marginal seats.

The Tories will be helped by a redistribution of constituency boundaries in England, but still face an uphill battle to win a secure majority. At the last general election the Conservatives won more votes in England than Labour, but 92 fewer seats, and the party still needs to build a big lead over Labour before it can hope to become the largest party in the Commons.

However, the Conservatives are beginning to eat into Labour's bedrock of support. One indication is that voters who failed to turn out in 2005 now say they intend to back Mr Cameron's party next time. That reverses a long-standing trend that saw Labour become the natural option for uncertain voters. Conservative and Lib Dem supporters are also more likely to say they intend to vote at the next election than Labour supporters.

Labour continues to retain a 13-point lead among voters aged under 24, but this group is less likely to vote than any other age range. Women are still more likely than men to back Labour, although both groups now show strong Tory leads. The poll suggests that Labour has retained the support of working-class voters but is suffering badly among middle-class voters, many of whom live in the sort of southern marginal seats that helped Mr Blair win power.

A year ago Labour had the backing of 39% of voters in economic category C1 and 35% of ABs. That has now fallen to 26% and 25%, with the Conservatives picking up support strongly.

· ICM interviewed a random sample of 1,007 adults over 18 by telephone on August 18-20. Interviews were conducted across the country and the results have been weighted to the profile of all adults.